8.5 1

Transformers – Simplifying the Complex

8.5 2

Section 8.5 Equations Reducible to Quadratic Forms

Recognizing Equations that are Quadratic Form Even Powers 4, 6, 8 and Up Radical Equations – square roots, fourth roots, etc Fractional Exponents ½, ¼, and Down Binomial Terms

8.5 3

Solving Quadratic Form EquationsAlways 3 Terms: ax2n + bxn + c = 0

If the 1st term’s variable part equals the square of the 2nd term’s variable part, you can use the following quadratic form technique:

Use a placeholder variable (u usually) to replace the 1st and 2nd term variables, solve as a quadratic, then back-substitute u with the variable and solve again.

ixandxxandx

solveuofplaceinxPut

uanduuu

solvenowuu

substitutethenuxux

xx

214

,

140)1)(4(

043

043

22

2

2

224

24

8.5 4

18

2499

232819

)1(2)8)(1(4)9(9

089

279

279

2

2

uu

u

u

uu

Practice – Even Powers

11

228

089

2

2

2

24

xmeansx

xmeansx

xu

xx

8.5 5

14

0)1)(4(0432

uu

uuuu

Practice - Radicals

falsex

xsox

xusoxu

xx

1

164

0432

8.5 6

12

0)1)(2(022

uu

uuuu

Practice – Fractional Exponents

11

82

02

2

31

31

32

31

31

32

31

32

2

msom

msom

musomu

mm

mm

8.5 7

532

5262

16366

)1(2)4)(1(4)6(6

0462

2

u

u

u

uu

Practice – Negative Exponents

53153

046

1

221

12

mso

m

musomu

mm

8.5 8

12

0)1)(2(022

uu

uuuu

Practice - Binomials

00

11

33

21

1

0211

2

2

2

2

2

222

xx

x

xx

x

xu

xx

8.5 9

What Next? Graphs of Quadratics Present Section 8.6